Articles containing proofs | Real transcendental numbers | Diophantine approximation | Irrational numbers | Mathematical constants

Liouville number

In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers (p, q) with q > 1 such that . Liouville numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers. They are precisely those transcendental numbers that can be more closely approximated by rational numbers than any algebraic irrational number. In 1844, Joseph Liouville showed that all Liouville numbers are transcendental, thus establishing the existence of transcendental numbers for the first time.It is known that π and e are not Liouville numbers. (Wikipedia).

Video thumbnail

A09 The Hamiltonian

Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.

From playlist Physics ONE

Video thumbnail

Lagrange Multipliers

Some problems using Lagrange Multipliers for optimization. In this video there are some technical problems beginning at about 9:10. The first problem is worked entirely, but the 2nd problem is interrupted.

From playlist Calc3Exam3Fall2013

Video thumbnail

Math 139 Fourier Analysis Lecture 10.1 L^2 convergence of Fourier Series

(Unfortunately I taped only part of this lecture.) Fourier series converges to the function in the L^2 sense.

From playlist Course 8: Fourier Analysis

Video thumbnail

Complex Numbers - Division Part 1 | Don't Memorise

How can one complex number be divided by another? Watch this video to know more To access all videos related to Complex Numbers, enrol in our full course now: https://bit.ly/ComplexNumbersDM In this video, we will learn: 0:00 Introduction 0:15 Complex number divided by real number 0:46

From playlist Complex Numbers

Video thumbnail

Liouville's number, the easiest transcendental and its clones (corrected reupload)

This is a corrected re-upload of a video from a couple of weeks ago. The original version contained one too many shortcut that I really should not have taken. Although only two viewers stumbled across this mess-up it really bothered me, and so here is the corrected version of the video, ho

From playlist Recent videos

Video thumbnail

Alexander Belavin - The correlation numbers in Minimal Liouville gravity

Alexander Belavin (Landau Institute et IITP, Moscou) The correlation numbers in Minimal Liouville gravity from Douglas string equation We continue the study of (q, p) Minimal Liouville Gravity with the help of Douglas string equation. Generalizing the earlier results we demonstrate that th

From playlist Conférence à la mémoire de Vadim Knizhnik

Video thumbnail

Conversion Arcs and 2,916,485,648,612,232,232,816 (MegaFavNumbers)

I'm sorry. The MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo

From playlist MegaFavNumbers

Video thumbnail

Norbert Verdier : When He was one hundred Years old!

In this Talks we will don’t speak about Joseph-Louis Lagrange (1736-1813) but about Lagrange’s reception at the nineteenth Century. “Who read Lagrange at this Times?”, “Why and How?”, “What does it mean being a mathematician or doing mathematics at this Century” are some of the questions o

From playlist Lagrange Days at CIRM

Video thumbnail

Colloquium MathAlp 2016 - Vincent Vargas

La théorie conforme des champs de Liouville en dimension 2 La théorie conforme des champs de Liouville fut introduite en 1981 par le physicien Polyakov dans le cadre de sa théorie des sommations sur les surfaces de Riemann. Bien que la théorie de Liouville est très étudiée dans le context

From playlist Colloquiums MathAlp

Video thumbnail

Sturm-Liouville Theory

An overview of some highlights of Sturm-Liouville Theory and its connections to Fourier and Legendre Series.

From playlist Mathematical Physics II Uploads

Video thumbnail

43,252,003,274,489,856,000 and 3,674,160 (#MegaFavNumbers)

#MegaFavNumbers If you have a favourite number over 1 million, post a video with you explaining why that number is so interesting.

From playlist MegaFavNumbers

Video thumbnail

Nikos Frantzikinakis: Ergodicity of the Liouville system implies the Chowla conjecture

Abstract: The Chowla conjecture asserts that the signs of the Liouville function are distributed randomly on the integers. Reinterpreted in the language of ergodic theory this conjecture asserts that the Liouville dynamical system is a Bernoulli system. We prove that ergodicity of the Liou

From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi

Video thumbnail

Transcendental numbers powered by Cantor's infinities

In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track

From playlist Recent videos

Video thumbnail

2021's Biggest Breakthroughs in Math and Computer Science

It was a big year. Researchers found a way to idealize deep neural networks using kernel machines—an important step toward opening these black boxes. There were major developments toward an answer about the nature of infinity. And a mathematician finally managed to model quantum gravity. R

From playlist Discoveries

Video thumbnail

Divisibility, Prime Numbers, and Prime Factorization

Now that we understand division, we can talk about divisibility. A number is divisible by another if their quotient is a whole number. The smaller number is a factor of the larger one, but are there numbers with no factors at all? There's some pretty surprising stuff in this one! Watch th

From playlist Mathematics (All Of It)

Video thumbnail

Jason Miller - 3/4 Equivalence of Liouville quantum gravity and the Brownian map

Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has roots in string theory and conformal field theory. The second is the Brownian map, which has roots in planar map combinatorics. We sho

From playlist Jason Miller - Equivalence of Liouville quantum gravity and the Brownian map

Video thumbnail

Dividing Complex Numbers Example

Dividing Complex Numbers Example Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys

From playlist Complex Numbers

Video thumbnail

Jason Miller - 4/4 Equivalence of Liouville quantum gravity and the Brownian map

Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has roots in string theory and conformal field theory. The second is the Brownian map, which has roots in planar map combinatorics. We sho

From playlist Jason Miller - Equivalence of Liouville quantum gravity and the Brownian map

Related pages

Transcendental number | Lebesgue measure | Absolute value | Diophantine approximation | If and only if | Continued fraction | Derivative | Tetration | John C. Oxtoby | Joseph Liouville | Algebraic number | Brjuno number | Thue–Morse sequence | Polynomial | Geometric series | Rational number | Cardinality of the continuum | Sequence | Dirichlet's approximation theorem | E (mathematical constant) | Lemma (mathematics) | Golden ratio | Mean value theorem | Dense set | Quadratic irrational number | Integer | Null set | Real number | Meagre set | Pi | Kurt Mahler | Infinity | Number theory | Series (mathematics) | Interval (mathematics) | Irrational number | Square root | Open set | Champernowne constant